Build a strong foundation in pure mathematics with key concepts including algebra, functions, and equations. Develop logical thinking, problem-solving skills, and confidence essential for academic success and advanced mathematical learning.
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High School Pure Mathematics Fundamentals is a comprehensive course designed to build strong foundations in Pure Mathematics, covering essential topics such as algebra skills, number systems, mathematical functions, geometry concepts, and trigonometry. This course helps learners develop confidence in advanced maths skills through structured lessons, practical examples, and effective problem-solving techniques.
This course introduces key mathematical principles including simultaneous linear equations, quadratic equations, co-ordinate geometry, sequences and series, binomial theorem, and functions. Learners will strengthen their algebra skills while exploring calculus basics such as derivatives, tangents and normals, stationary points, curve sketching, and integration to improve mathematical understanding and accuracy.
Designed for students seeking to enhance their mathematical abilities, this course develops logical thinking, analytical skills, and confidence with mathematical proofs and problem solving. By mastering core concepts in calculus, geometry, and mathematical functions, learners will gain the knowledge required to progress towards higher-level mathematics and academic success.
After completing the High School Pure Mathematics Fundamentals course assessment, you will be eligible to receive a CPD-accredited certificate worth £9 from One Education to demonstrate your achievement.
The certificate is also available as a printed hard copy delivered by post for £15.
High School Pure Mathematics Fundamentals introduces learners to the essential concepts of pure mathematics, including algebra skills, calculus basics, geometry concepts, trigonometry, mathematical functions, and number systems. This course explores mathematical reasoning, problem-solving techniques, and proof methods to help learners develop a strong foundation in advanced maths skills.
Studying High School Pure Mathematics Fundamentals enhances analytical thinking, logical reasoning, and confidence in applying mathematical principles. The course supports students preparing for further education, examinations, and STEM-related fields by strengthening their understanding of core mathematical concepts, problem-solving approaches, and the techniques required for higher-level mathematics.
The High School Pure Mathematics Fundamentals course has a total study time of 1 day, 3 hours. This comprehensive programme is designed for flexible learning, allowing learners to progress at their own pace while developing pure mathematics skills, including algebra, calculus basics, geometry concepts, trigonometry, mathematical functions, number systems, mathematical proofs, problem-solving techniques, advanced maths skills, and essential foundations for higher-level mathematics.
The High School Pure Mathematics Fundamentals course requirements are simple and suitable for learners with a basic mathematical background. Participants should have an understanding of fundamental arithmetic and numeracy, an interest in developing algebra, calculus, geometry, and problem-solving skills, and a willingness to explore advanced mathematical concepts. Access to an internet-enabled device and commitment to regular study are recommended for effective learning and successful course completion.
This course introduces the key concepts of pure mathematics, covering algebra skills, calculus basics, geometry concepts, trigonometry, mathematical functions, number systems, mathematical proofs, problem-solving techniques, and advanced maths skills required for further study.
No. It is suitable for students, beginners, and anyone looking to strengthen their mathematical foundation, improve analytical thinking, and develop confidence in higher-level mathematics.
The course is delivered online, allowing you to learn at your own pace and build essential pure mathematics knowledge through flexible and structured lessons.
Yes. Mathematical exercises, problem-solving activities, algebra tasks, geometry questions, calculus practice, proof-based exercises, and quizzes may be included to reinforce learning.
You will receive a certificate of completion after successfully finishing the course.
This course supports further academic and professional development in mathematics, engineering, computer science, finance, data analysis, science, education, and other fields requiring strong analytical and quantitative skills.
| Introduction | |||
| About Course | 00:02:00 | ||
| Quick Guide | 00:01:00 | ||
| Essential Revision-1 | |||
| Topics of Essential Revision – 1 | 00:00:00 | ||
| Negative numbers and operations on Integers | 00:14:00 | ||
| The rules of Indices in Algebra | 00:11:00 | ||
| Working with indices Part 1 | 00:10:00 | ||
| Working with indices Part 2 | 00:08:00 | ||
| Fractional Indices | 00:12:00 | ||
| What are Polynomials? | 00:07:00 | ||
| Writing statements in Algebraic Form | 00:06:00 | ||
| Simplification using BODMAS | 00:08:00 | ||
| Distributive Property | 00:07:00 | ||
| Addition of Algebraic expressions | 00:13:00 | ||
| Subtraction of Algebraic expressions | 00:12:00 | ||
| Multiplication of Algebraic Expressions Part 1 | 00:05:00 | ||
| Multiplication of Algebraic Expressions Part 2 | 00:05:00 | ||
| Multiplication of Algebraic Expressions Part 3 | 00:06:00 | ||
| Division of algebraic expressions Part 1 | 00:11:00 | ||
| Division of algebraic expressions Part 2 | 00:10:00 | ||
| Division of algebraic expressions Part 3 | 00:07:00 | ||
| Essential Revision-2 ( Different Methods Of Factorization) | |||
| Topics of Essential Revision – 2 | 00:00:00 | ||
| Factorization by method of common factor | 00:13:00 | ||
| Factorization by regrouping the terms | 00:10:00 | ||
| Factorization by difference of two squares | 00:11:00 | ||
| Factorization using identity (a + b) ² and (a – b) ² | 00:10:00 | ||
| Factorization using identity (a + b + c) ² | 00:05:00 | ||
| Factorization by middle term split Part 1 | 00:12:00 | ||
| Factorization by middle term split Part 2 | 00:09:00 | ||
| Simultaneous Linear Equations | |||
| Simultaneous Linear Equations | 00:07:00 | ||
| Graphical Method | 00:06:00 | ||
| Graphical method Continued | 00:11:00 | ||
| Elimination by substitution Method | 00:09:00 | ||
| Equating the coefficients Method | 00:11:00 | ||
| Cross Multiplication | 00:10:00 | ||
| Equations Reducible to Linear Equations-1 | 00:08:00 | ||
| Equations Reducible to Linear Equations-2 | 00:14:00 | ||
| Quadratic Equations | |||
| Introduction to Quadratic Equations | 00:05:00 | ||
| Solving Quadratic Equations by Factorization method | 00:09:00 | ||
| Writing in completed square form | 00:07:00 | ||
| Solving by completed square method | 00:08:00 | ||
| Sketching of Quadratic Graphs | 00:12:00 | ||
| Quadratic graphs using Transformations | 00:06:00 | ||
| Quadratic inequalities | 00:11:00 | ||
| Deriving Quadratic formula | 00:05:00 | ||
| Solving problems using Quadratic Formula | 00:06:00 | ||
| Nature of Roots Part – 1 | 00:05:00 | ||
| Nature of roots Part – 2 | 00:12:00 | ||
| Downloadable Resources | 00:00:00 | ||
| Co-ordinate Geometry | |||
| Distance formula | 00:18:00 | ||
| Mid point formula | 00:05:00 | ||
| Gradient of a line | 00:11:00 | ||
| Graphing using gradient and y intercept | 00:03:00 | ||
| Some standard lines | 00:05:00 | ||
| Slope intercept form y = m x +c | 00:06:00 | ||
| Point slope form and two point form | 00:11:00 | ||
| Intersection of line and parabola | 00:10:00 | ||
| Past Papers Problems Part 1 | 00:09:00 | ||
| Past Papers Problems Part 2 | 00:11:00 | ||
| Past Papers Problems Part 3 | 00:09:00 | ||
| Past Papers Problems Part 4 | 00:12:00 | ||
| Past Papers Problems Part 5 | 00:12:00 | ||
| Downloadable Resources | 00:00:00 | ||
| Sequence and Series | |||
| Sequence and series ( video) | 00:08:00 | ||
| Arithmetic Sequence | 00:10:00 | ||
| General term of an A.P. | 00:07:00 | ||
| Finding given term is which term | 00:05:00 | ||
| Writing sequence when two terms are known | 00:08:00 | ||
| Condition for three terms to be in A.P. | 00:05:00 | ||
| Sum to n terms of A.P. | 00:06:00 | ||
| Practice Problems 1 (A.P.) | 00:09:00 | ||
| Practice problems 2 (A.P.) | 00:07:00 | ||
| Practice problems 3 (A.P.) | 00:07:00 | ||
| Practice problems 4 (A.P.) | 00:11:00 | ||
| Geometric Progressions | 00:12:00 | ||
| Sum to n terms in G.P. | 00:14:00 | ||
| Sum to infinite Terms in G.P. | 00:13:00 | ||
| Practice Problems 1 (GP) | 00:15:00 | ||
| Practice Problems 2 (GP) | 00:12:00 | ||
| Practice Problems 3 (GP) | 00:07:00 | ||
| Practice Problems based on AP and GP both | 00:15:00 | ||
| Past papers problems 1 | 00:17:00 | ||
| Past papers problems 2 | 00:10:00 | ||
| Past papers problems 3 | 00:11:00 | ||
| Downloadable Resources | 00:00:00 | ||
| Geometric Progressions – Resources | 00:00:00 | ||
| Binomial Theorem | |||
| What is Factorial? | 00:07:00 | ||
| n-choose –r problems | 00:07:00 | ||
| Properties of n – choose -r | 00:05:00 | ||
| Binomial Theorem for positive index | 00:20:00 | ||
| Expanding using Binomial Theorem | 00:11:00 | ||
| Finding the indicated term in the Binomial expansion | 00:11:00 | ||
| Finding the indicated term from end | 00:09:00 | ||
| Finding the coefficient for given exponent (index) of the variable | 00:09:00 | ||
| Finding the term independent of variable | 00:05:00 | ||
| Expanding in increasing and decreasing powers of x | 00:09:00 | ||
| Practice problems 1 | 00:12:00 | ||
| Practice Problems 2 | 00:09:00 | ||
| Practice problems 3 | 00:10:00 | ||
| Past papers problems 1 | 00:15:00 | ||
| Past Paper problems 2 | 00:13:00 | ||
| Past Paper problems 3 | 00:09:00 | ||
| Downloadable Resources | 00:00:00 | ||
| Functions | |||
| What is Function? | 00:08:00 | ||
| Vertical Line Test | 00:04:00 | ||
| Value of a Function Graphically | 00:08:00 | ||
| Domain Range of a function Algebraically | 00:14:00 | ||
| Domain Range of a function Graphically | 00:07:00 | ||
| Even & Odd Functions | 00:07:00 | ||
| One to one Function | 00:05:00 | ||
| Composite Functions | 00:09:00 | ||
| How to draw Rational Functions- 1 | 00:05:00 | ||
| How to draw Rational Functions- 2 | 00:10:00 | ||
| Inverse of a function Algebraically | 00:05:00 | ||
| Inverse of a function Graphically | 00:09:00 | ||
| Practice Problems 1 | 00:16:00 | ||
| Practice Problems 2 | 00:11:00 | ||
| Downloadable Resources | 00:00:00 | ||
| Derivatives | |||
| What is Derivative? | 00:08:00 | ||
| Derivation of formula for Derivative | 00:06:00 | ||
| Differentiation by definition or First Principle | 00:07:00 | ||
| Power Rule | 00:22:00 | ||
| Practice Problems on Power Rule 1 | 00:07:00 | ||
| Practice Problems on Power Rule 2 | 00:07:00 | ||
| Practice Problems on Power Rule 3 | 00:05:00 | ||
| Practice Problems on Power Rule 4 | 00:13:00 | ||
| Practice Problems on Power Rule 5 | 00:08:00 | ||
| Downloadable Resources | 00:00:00 | ||
| Tangents and Normals | |||
| Tangents and Normals- Basics | 00:13:00 | ||
| Practice- Tangents and Normals Part 1 | 00:16:00 | ||
| Practice- Tangents and Normals Part 2 | 00:13:00 | ||
| Practice- Tangents and Normals Part 3 | 00:11:00 | ||
| Practice- Tangents and Normals Part 4 | 00:14:00 | ||
| Downloadable Resources | 00:00:00 | ||
| Stationary Points & Curve Sketching | |||
| Stationary Points – Basics | 00:13:00 | ||
| Practice- Increasing Decreasing & Maxima Minima part 1 | 00:11:00 | ||
| Practice- Increasing Decreasing & Maxima Minima part 2 | 00:12:00 | ||
| Practice- Increasing Decreasing & Maxima Minima part 3 | 00:10:00 | ||
| Downloadable Resources | 00:00:00 | ||
| Second Derivative Test (Maximum & Minimum Points) | |||
| Concavity-Basics | 00:02:00 | ||
| Concavity & Second Derivative | 00:08:00 | ||
| Second Derivative Test | 00:09:00 | ||
| Practice Problems on second derivative | 00:04:00 | ||
| Practice Problem of Maxima Minima using second derivative test Part 1 | 00:17:00 | ||
| Practice Problem of Maxima Minima using second derivative test Part 2 | 00:10:00 | ||
| Practice Problem of Maxima Minima using second derivative test Part 3 | 00:07:00 | ||
| Practice Problem of Maxima Minima using second derivative test Part 4 | 00:07:00 | ||
| Applications of Maxima and Minima Part 1 | 00:09:00 | ||
| Applications of Maxima and Minima Part 2 | 00:07:00 | ||
| Applications of Maxima and Minima Part 3 | 00:10:00 | ||
| Applications of Maxima and Minima Part 4 | 00:09:00 | ||
| Applications of Maxima and Minima Part 5 | 00:10:00 | ||
| Applications of Maxima and Minima Part 6 | 00:08:00 | ||
| Past Paper Problems on applications of maxima and minima Part 1 | 00:09:00 | ||
| Past Paper Problems on applications of maxima and minima Part 2 | 00:09:00 | ||
| Past Paper Problems on applications of maxima and minima Part 3 | 00:08:00 | ||
| Past Paper Problems on applications of maxima and minima Part 4 | 00:07:00 | ||
| Chain Rule | 00:12:00 | ||
| Rate of change part 1 | 00:05:00 | ||
| Rate of change part 2 | 00:10:00 | ||
| Rate of change part 3 | 00:07:00 | ||
| Past Paper Problems using chain rule -1 | 00:06:00 | ||
| Past Paper Problems using chain rule -2 | 00:07:00 | ||
| Past Paper Problems using chain rule – 3 | 00:07:00 | ||
| Past Paper Problems using chain rule – 4 | 00:04:00 | ||
| Downloadable Resources | 00:00:00 | ||
| Integration | |||
| What is Integration? | 00:12:00 | ||
| Practice Questions 1 | 00:06:00 | ||
| Practice Questions 2 | 00:09:00 | ||
| Practice Questions 3 | 00:09:00 | ||
| Fundamental Theorem of Calculus | 00:09:00 | ||
| What is Definite Integration? | 00:10:00 | ||
| Finding Definite Integration | 00:09:00 | ||
| Practice Questions on Definite Integration 1 | 00:10:00 | ||
| Practice Questions on Definite Integration 2 | 00:10:00 | ||
| Practice Questions on Definite Integration 3 | 00:15:00 | ||
| Area below x-axis | 00:12:00 | ||
| Practice Problems on Area below x-axis 1 | 00:11:00 | ||
| Practice Problems on Area below x-axis 2 | 00:13:00 | ||
| Practice Problems on Area below x-axis 3 | 00:09:00 | ||
| Practice Problems on Area below x-axis 4 | 00:07:00 | ||
| Area between two curves (Basics) | 00:15:00 | ||
| Practice Problems on Area between two curves 1 | 00:06:00 | ||
| Practice Problems on Area between two curves 2 | 00:13:00 | ||
| Practice Problems on Area between two curves 3 | 00:12:00 | ||
| Practice Problems on Area between two curves 4 | 00:10:00 | ||
| Practice Problems on Area between two curves 5 | 00:13:00 | ||
| The Reverse Chain Rule- Indefinite Integration | 00:06:00 | ||
| The Reverse Chain Rule- Definite Integration | 00:05:00 | ||
| Practice Problems on The Reverse Chain Rule | 00:09:00 | ||
| Improper Integrals | 00:06:00 | ||
| Volumes by Integration | 00:08:00 | ||
| Practice Problems on Volumes by Integration-1 | 00:04:00 | ||
| Practice Problems on Volumes by Integration-2 | 00:04:00 | ||
| Order Your Certificate | |||
| Order Your Certificate Now | 00:00:00 | ||
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